Many English voters are angry that England-only laws and policies can be decided by MPs from areas with devolved legislatures, ministers have been told. Photograph: AP

English MPs should be given far greater control over laws that affect only England to tackle growing resentment among voters about devolution elsewhere in the UK, ministers have been told.

A commission headed by Sir William McKay, a former clerk of the House of Commons, has told the government that the Commons should restrict the rights of Scottish, Welsh and Northern Irish MPs to influence or determine purely English legislation in future.

In a report to the Cabinet Office published later on Monday, the commission says there is consistent evidence that English voters were are annoyed that England-only laws and policies can be voted on or decided by MPs from areas with devolved legislatures, such as the Scottish parliament.

It has released new poll findings, based on research by the Institute of Public Policy Research, which show that 81% of English voters either agree or strongly agree that Scottish MPs should not vote on English laws. However, that poll also found that only 20% of voters wanted a separate English parliament.

The McKay commission insisted that, to avoid destabilising parliament and creating two classes of MP, their proposals would not allow English MPs a right of veto over laws passed by the government. But it said the overarching principle with England-only bills was that any government should act with the consent of English MPs, unless it had good reason not to.

"The status quo clearly cannot be sustained," McKay said. "Our proposals retain the right of a UK-wide majority to make the final decisions where they believe UK interests or those of a part of the UK other than England should prevail. We expect that governments will prefer compromise to conflict."

The commission says a number of procedures can be used in the early stages of a bill, including: a grand committee of all English MPs; a special bill committee set up to amend legislation; or separate votes on different clauses that might be England-only. In some cases, where a bill also affected Wales, the same measures could be used.

The report will provoke a backlash from Labour MPs who fear it will strengthen Tory control over English legislation and stoke up nationalist sentiment in the runup to the Scottish independence referendum in September 2014 – an anxiety shared privately by UK government ministers.

While it plans to increase Scottish and Welsh devolution, Labour is suspicious of the government's motives, and did not submit written or oral evidence to the McKay commission. It noted that the McKay report was just "another contribution to the debate".

A Cabinet Office spokesman said it was "a very important issue. We will give the report very serious consideration before we respond substantively."

Ken Clarke, who recommended English-only votes on early stages of bills in an official Conservative report before the last election, said he believed action was needed before the 2015 general election.

"It's a good idea to solve it now," Clarke said. "What we don't want is some close-run election with some government being elected with a tiny majority and arguments breaking out as to whether various things are being carried by the votes of people from constituencies that aren't faintly affected."

The inquiry was set up under the 2010 coalition agreement to meet demands from Tory backbenchers and senior party figures such as Clarke and Sir Malcolm Rifkind for action to tackle the so-called West Lothian question, because of the growing powers of the Scottish and Welsh parliaments.

A paradox named after the former MP for West Lothian, Tam Dalyell, it asks why an MP from Scotland should be free to vote on English health legislation at Westminster but no English MP could vote on Scottish health matters now they are controlled at Holyrood.

The controversy erupted several times under Labour. Once when John Reid, the Labour MP for Hamilton and North Bellshill became English health secretary in 2003, and when Scottish Labour backbenchers helped push through legislation on which English Labour MPs were rebelling, on tuition fees and foundation hospitals.

The commission said these occasions were actually rare: it believed the real task was to strengthen English democracy and Westminster's accountability to England's voters in the post-devolution era.

Professor Charlie Jeffrey, a commission member and a vice principal at Edinburgh University, said: "Our concern was essentially to recognise what we think is a need for England's voice to heard and to be seen to be heard, because there's a danger that the disconnect we see in English public opinion could intensify, if that opportunity isn't given."